Chromatography apparatus with direct heating of the capillary column

ABSTRACT

A method and an apparatus for chromatography are described, wherein at least one element in electrically conductive material is provided to heat the capillary column in a direct way and wherein the control of the temperature is carried out according to a mathematical model having a component of predictive type, or Feed Forward type, that describes the thermodynamic behavior of the assembly comprising the electrically conductive element and the column at least as a function of the thermal resistance and the thermal capacity of the assembly thus constituted in order to regulate the supply of electrical power supplied to the conductive element.

TECHNICAL FIELD

[0001] The present invention relates to apparatus for chromatography inwhich the capillary column is heated directly and to a method ofcontrolling the temperature of the capillary column.

BACKGROUND ART

[0002] It is known in the art that direct heating of the column confersvarious advantages, among which is a considerable reduction in thequantity of electrical power required to heat the column by means of anelement made of electrically conductive material which encircles thesame capillary column.

[0003] An example of a portable gas chromatography apparatus with directheating of the column is described in U.S. Pat. No. 5,611,846 by Overtonet al. In order to directly heat the column, this document suggestsinserting the column into a sheath together with a conductive filament,or inserting the column directly into a tube made of conductivematerial. The hypothesis of using columns covered with conductivematerial—such as, for example, columns in fused silica covered with athin layer of aluminum—had already been rejected because of frequentbreakage of the column or the covering conductor due to the differentcoefficients of thermal expansion of the materials.

[0004] As a temperature sensor, the Overton patent suggests to use afilament made of conductive material inserted into the sheath or theconductive tube in close contact with the column but insulatedelectrically from the other conductive element (tube or filament) usedto heat the column. A control device able to determine the temperatureof the conductor as a function of its resistance is employed to regulatethe heating of the column. The control device cyclically compares theset temperature with that calculated on the basis of the temperaturesensor signal and corrects the power supplied to the heating conductorby varying the voltage applied to the same. Moreover, the possibility ofusing the same heating conductor as temperature sensor is alsosuggested, without however specifying what kind of control device couldbe suitable for this particular embodiment.

[0005] While not specifying which type of control was used in the systemof the cited US patent, it was asserted that the system is able tocontrol a temperature ramps of slope up to 10° C./sec. This parameterconfirms that the direct heating of the column can be efficient from thepoint of view of the rapidity of response of the system, but isopportune to point out that obtaining similar heating speeds with aninadequate control device could compromise the stability and theprecision of the system in its entirety.

[0006] In fact, it has been subsequently found that this type of systemhas shortcomings related to both the precision of temperaturemeasurement with respect to conventional chromatography apparatus withoven heating, and to the repeatability of the set temperature profilesfor identical analyses (see “Novel Column Heater for Fast Capillary GasChromatography”; Overton et al—Journal of Chromatographic Science—Vol.34—December 1996, for example).

[0007] U.S. Pat. No. 5,114,439 by Yost et al describes a chromatographyapparatus in which the column is covered with a film of conductivematerial. This document confirms substantially the effectiveness of thecolumn direct heating technology, but it is opportune to emphasize thatthe use of columns covered with conductive films involves thedisadvantages already identified by Overton referred to previously. Astemperature control device, the Yost patent suggests the use of aPID-type industrial controller to control by feedback the electricalsupply to the conductor associated with the column.

[0008] A system for heating the column by means of a tube conductorwhich contains the same column is illustrated in U.S. Pat. No. 5,808,178and in the corresponding international patent application n. WO 97/14957in the name of Thermedics. The temperature control system alternatescycles of supplying constant high voltage to heat the tube conductor,with measurement cycles of more limited constant voltage to measure theresistance of the tube conductor and, consequently, the temperature ofthe tube/column system. Moreover, the use of standard PI or PID typestandard industrial controllers is suggested as an improvement of asimilar system.

[0009] However, it should be noted that even PID type standardcontrollers are inadequate to guarantee the necessary temperaturecontrol precision when particularly high heating speeds are applied.

[0010] A slightly improved column temperature control system isdescribed in U.S. Pat. No. 5,005,399 by Holtzclaw et al. Also in thiscase, the heating system provides for the use of a column covered with aconductive film, therefore subject to all the disadvantages alreadypreviously cited. However, to control the heating temperature, a controldevice is suggested in which a pseudo-derivative correction factor isintroduced into the feedback control of the temperature or, rather, ofthe voltage applied to the conductive material which covers the column.One of the main disadvantages of this system lies in the fact that, tomaintain the correct operation of the column within the specified limitsof error (±1° C.), particularly precise calibration of the gain of everycomponent of the control system is required. The calibration operationsnecessarily demand a certain skill and experience, and they arenecessary every time the column is replaced.

[0011] The object of the present invention is to propose achromatography apparatus with direct heating of the column that givesparticularly precise control of the temperature of the column.

[0012] Another object of the present invention is to propose achromatography apparatus with direct heating of the column that canguarantee high response speed, maintaining in any case the necessaryprecision with respect to the set temperature profiles, be they linearor not linear (e.g. exponential and polynomial)

DISCLOSURE of THE INVENTION

[0013] These objects are achieved by the present invention, that relatesto a chromatography apparatus, of the type comprising at least onecapillary column and means to control the temperature of the column,characterized by comprising at least one element made of electricallyconductive material to heat directly the capillary column, and by meansfor controlling the temperature of the capillary column comprising acontrol device operating according to a mathematical model having onecomponent of predictive type, or of Feed Forward type, which describesthe thermodynamic behavior of the assembly comprising the electricallyconducting element and the column at least as a function of the thermalresistance and the thermal capacity of the cited assembly to regulatethe supply of electrical energy to the conductive element.

[0014] The behavior of the conductive element is therefore simulated byone model component that takes account of the thermodynamiccharacteristics of the conductor/column assembly to determine what powermust be applied to the conductive element to obtain the pre-establishedtemperature at a given time. That in particular allows a fast responseto unexpected variations of the temperature profiles set up for theanalysis.

[0015] Beyond the predictive or Feed Forward type component, the modelcomprises also one component preferably of corrective or Feed Back type,to correct any errors of temperature that may be introduced by thepredictive component of the model.

[0016] Contrary to what happens in the known art, in which the controlsystems operate in feedback alone trying continuously to reach a seriesof equilibrium conditions, the system of the present invention operatesaccording to a mathematical model that describes the thermodynamicbehavior of the system under the form of a transfer function determinedby two very well-defined algorithms.

[0017] The advantage of this approach is given by the greatercontribution of power being determined a priori by the Feed Forward typemodel component, while a smaller contribution of power is determined bythe Feed Back type model component on the basis of the temperatureerror. In this way, the power determined by the Feed Back type model isconsiderably reduced and the control consequently turns out to be themuch more stable.

[0018] However, It must be taken into account that rapidity andprecision are requirements that may be in conflict. In order to obtainrapidity of response it is necessary to supply instantaneouslyconsiderable power to the conductive element, while to obtain a certainprecision it is opportune to supply limited amounts of power to theheating element over relatively longer times. Therefore, the powersdetermined on the basis of the two model components can also be“weighted” as a function of the requirement that needs to be privilegedin any determined application

[0019] According to a preferential aspect of the present invention, thetemperature control device is able to cyclically update the parametersof the mathematical model and, in particular, at least the values ofthermal capacity and thermal resistance.

[0020] This gives particularly high precision as far as the regulationof the temperature of the column directly heated by the conductiveelement is concerned.

[0021] In order to detect the temperature of the column, it ispreferably used the same element in electrically conductive materialdestined for the heating of the column. The column and the conductiveelement are disposed in one covering sheath, in conditions of closemutual contact for all the length contained inside the same sheath. Thisallows effective thermal exchange to be maintained between conductiveelement and column for all their length and to limit thermal losses.

[0022] The covering sheath is preferably made of electrically insulatingmaterial and the column/conductor/sheath assembly can be wrapped incoils without undesired short circuits occurring that might prejudicethe correct operation of the system.

[0023] In a possible embodiment of the invention, the element inelectrically conductive material is made in the form of a filament.However, it must be understood that the system and the method forcontrolling the temperature according to the invention are applicable toany type of directly heated column assembly in which it is present aconductive element made according to a different form.

[0024] Moreover, the control system adopted in the apparatus accordingto the present invention can also be used in the case in which a furtherconductive element is used, separate from the heating element, to detectthe temperature of the column.

[0025] The covering sheath is made from electrically insulating materialand is preferably able to resist high temperatures, such as ceramicfibers or similar, for example.

[0026] Alternatively, the sheath can also be made from athermo-shrinking type of material. The materials currently known havingsuch characteristic, such as those known by the commercial name Teflon™for example, can not support high temperatures much above 200° C., butthis does allow the filament and the column to be easily introduced intothe inside of the sheath before the assembly thus formed is subjected toheating to allow the contraction of the sheath and to obtain the desiredclose contact between column and filament.

[0027] The invention further relates to a method for controlling thetemperature of a capillary column in a chromatography apparatus,characterized by providing for the use of at least one element made ofelectrically conductive material to heat directly the capillary column,and by the control of the temperature being carried out according to amathematical model having a component of the predictive type, or FeedForward type, which describes the thermodynamic behavior of the assemblycomprising the electrically conductive element and the column at leastas a function of the thermal resistance and the thermal capacity of saidassembly to regulate the supply of electrical power to the conductiveelement.

BRIEF DESCRIPTION of DRAWINGS

[0028] Further features and advantages of the present invention willbecome clearer from the description that follows, which is made forillustrative and not limiting purpose with reference to the attacheddrawings, in which:

[0029]FIG. 1 is a block diagram of a system for temperature control in achromatography apparatus according to the present invention;

[0030]FIG. 2 is a circuit diagram of the system shown in FIG. 1;

[0031]FIG. 3 is a cross-section view that shows one possible embodimentof the assembly comprising a capillary column and a conductive filamentfor heating the same;

[0032]FIGS. 4A and 4B illustrate schematically the behavior of thecolumn/filament assembly during operation of the apparatus according tothe present invention;

[0033]FIG. 5 is a cross-section view that illustrates another possibleembodiment of the assembly comprising a capillary column and aconductive filament for the heating of the same;

[0034]FIG. 6 is a functional diagram showing the logic of the model of acontrol system for an apparatus according to the present invention;

[0035]FIG. 7 is a diagram of the temperature profile generator block ofthe model in FIG. 6;

[0036]FIG. 8 is a diagram of the Feed Forward block of the model in FIG.6;

[0037]FIG. 9 is a diagram of the Feed Back block of the model in FIG. 6;

[0038]FIG. 10 is a diagram of the voltage actuator block of the model inFIG. 6;

[0039]FIG. 11 is a diagram that schematically illustrates the change oftemperature over time compared with a simple temperature profile; and

[0040]FIG. 12 shows a chromatogram of a test analysis carried out with asystem according to the present invention.

MODES FOR CARRYING OUT THE INVENTION

[0041] The temperature control system illustrated in FIG. 1 comprises afunctional block 10 able to memorize and update the relative parametersof the thermodynamic model of the assembly constituted by a conductiveelement 100, made for example in the form of a filament, and by acapillary column 200 (FIGS. from 3 to 5).

[0042] According to the embodiment shown in FIG. 3, the conductivefilament 100, made for example from metal such as nickel or otherconductive material, is placed in close contact with the capillarycolumn 200, made of fused silica for example, inside a sheath 300. Inthis case, filament 100 is also used as temperature sensor.

[0043] The covering sheath 300 is produced in electrically insulatingmaterial, such as, for example, ceramic fibers. Alternatively, materialscan also be employed with characteristics compatible with particularrequirements, such as a thermo-shrinking material (e.g. Teflon™), orpolyamide or the like. The use of a thermo-shrinking type material couldfacilitate the fabrication of the assembly constituted by filament 100,column 200 and sheath 300, even if currently the greater part of theknown thermo-shrinking materials are not particularly resistant to hightemperatures.

[0044] The use of an electrically insulating material for the sheathallows the assembly comprising the filament, the column and the samesheath to be wrapped in coils without any contact occurring betweenvarious parts of the same filament, contact that would unavoidablyprejudice the operation of the system.

[0045] The chosen configuration for filament 100 and column 200 insertedinto sheath 300 allows the different expansions between filament 100 andcolumn 200 to be compensated in function of the temperature even in thecase in which the sheath/filament/column assembly is wrapped in coils.

[0046]FIG. 4A shows the assembly at room temperature starting from ahypothetical condition of alignment of the straight line A that joinsthe centers of column 200 and filament 100 with respect to a horizontalplane P on which lies the straight line A corresponding to a givensection, plane P on which also lies substantially one coil of thesheath/filament/column assembly in wrapped condition. Following theheating of the conductive filament 100, the greater thermal expansion offilament 100 transforms into a deformation of the assembly shown in FIG.4B. In practice, filament 100 rotates with respect to column 200 causingthe straight line A that connects the two centers to be inclined at anangle β with respect to plane P as a function of the difference oflinear expansion to which filament and column in each coil are subject.The assembly is therefore equipped with an elastic geometry in which thedifferent linear expansions of the conductive element 100 and column 200are transformed into deformations that involve only slight variations ofthe mutual position of the conductive element and the column inside thesheath.

[0047] Returning again to FIG. 1, functional block 10 receivescyclically the information DT_(set) and T_(set) relative to the desiredtemperature profile, information coming from a data processing unit ordata input device, for example, or from a dedicated controller alreadypresent in the chromatography apparatus (not shown).

[0048] In particular, DT_(set) represents the desired temperaturevariation, i.e. the desired heating speed, while T_(set) represents theinstantaneous value of the set up temperature. Information on theambient temperature T_(amb) also reaches functional block 10 supplied bya suitable sensor 15. The separate supply of values DT_(set) and T_(set)allows advantageously even temperature profiles with non-linearfeatures, for example profiles of temperature with exponential orpolynomial features, to be set up and followed with particularprecision.

[0049] The output 11 of the functional block 10 drives a power unit 20able to supply to the heating element, such as filament 100 inconductive material, the voltage (and therefore the power) necessary toconstantly follow the set up temperature profile with particularprecision.

[0050] From the same filament 100, the voltage between terminals of thefilament V_(C) and current that circulates in it I_(C) are measuredevery instant. These data are sent to a first calculation block 40 ableto determine the instantaneous resistance R_(c) of the filament thatheats the column in relation to the data received by applying the wellknown Ohm's law, which gives in this case:

R _(c) =V _(c) /I _(c)  (1)

[0051] The Rc value thus calculated is sent in its turn to a secondcalculation block 50 that determines the instantaneous temperature I_(c)of column 200 placed in contact with filament 100. Ic can be calculatedstarting from the known relation that links the resistance of filament100 to the temperature, i.e.:

R _(c) =R _(ref)*[1+α*(T _(c) −T _(ref))]  (2)

[0052] in which R_(C) is the resistance of the filament at temperatureT_(c), R_(ref) is the resistance of the same conductor at a referencetemperature T_(ref) and α is the coefficient of resistivity of thematerial from which the conductive filament is made as a function of thetemperature. Resolving the equation (2) for T_(c) gives:

T _(c) =[R _(c) −R _(ref)*(1−α*T _(ref))]/α*R _(ref)  (3)

[0053] It is known that the value of the coefficient α can be consideredconstant only in a limited temperature range, but it is worth to takeinto account that this coefficient also varies as a function of thetemperature. Therefore, T_(c) according to equation (3) can for examplebe calculated on the basis of values of T_(c) estimated and memorized ina table, using interpolation techniques for intermediate values.Alternatively, the values of coefficient α for each temperature can bememorized in a table or the variations Δα as a function of thetemperature with respect to the value α considered constant.

[0054] The same calculation can be done for the value p of the specificresistivity of the material instead of the same resistance, taking intoaccount the relation:

R=ρ*l/s  (4)

[0055] In which is the length of the conductive filament and s is itssection. The value T_(c) thus determined from second calculation block50 is cyclically compared in 60 with the value of the set-pointtemperature T_(set) in such way as to determine the temperature errorErr_(T) between the set-point temperature and that effectively obtainedat a given step.

[0056] The value corresponding to the temperature error Err_(T) is takenas input to a block 70 that has the function of “observer”, together toDT_(set) value of the derivative of the temperature profile to befollowed.

[0057] According to these data received as input, i.e. in function ofthe temperature error and of the trend of the same temperature in thetime, the observer block 70 determines the new values of thermalresistance R_(th) and thermal capacity C_(th) that must be sent as inputto functional block 10 in order to update the parameters of themathematical model that describes the thermodynamic behavior of filament100 and to permit correct control of the power unit 20.

[0058] All the cyclical operations are repeated at high frequency, forexample with a period less than a millisecond, so as to obtain highprecision of reproduction of the desired temperature profile.

[0059] Beyond guaranteeing high precision, the control system accordingto the present invention allows—even at operational speed—temperatureprofiles with particularly high heating speeds to be followed easily(for example heating speed up to approximately 25° C./s) whilemaintaining a good precision.

[0060] In order to obtain the initial parameters of the mathematicalmodel it is possible for example to determine the resistance of filament100 at a first pre-established temperature and therefore to establishthe variation of the resistance of the filament when the same is takento a second pre-established temperature, different from the previousone, according to a pre-established way, for example by applying a stepvariation to the power supplied to the heating element. This allows theinitial values of thermal resistance and thermal capacity of the modelto be found, as well as the length of the column to be calculated if thecross-section of filament 100 is known or, if this is not known, forexample, the effective length of column 200 to be determined, or toverify that the length of column 200 associated with heating filament100 is effectively that pre-established.

[0061]FIG. 6 shows a functional diagram of a model that can be appliedto every iteration of the system. The blocks shown in this diagram,taken as a whole, control the power supplied to the system, in the formof a supply voltage V_(sup), and therefore control the temperature ofthe column.

[0062] The model comprises for example a DATA INPUT block, indicated byreference 500, that acquires a number of input variables at step n−1 anda TPG (Temperatures Profiles Generator) block, indicated by reference510, which generates the desired temperature profiles, i.e. not onlylinear profiles of temperature (isotherms and ramps) but alsoexponential or polynomial profiles.

[0063] The data coming from blocks 500 and 510 are supplied to blocks530 (FF Model) and 550 (FB Model) which represent respectively thepredictive component of Feed Forward type and the corrective componentof Feed Back type of the model. The latter calculate what power willhave to be supplied to the heating element of the column at step n byblock 570 (Voltage Actuator) which is the actuator of the supply voltageV_(sup). In other words, V_(sup) ^((n)) represents the supply voltagethat must be supplied to the system in its entirety, not only to supplypower to the column and thus obtain the T_(set) ^((n)), temperature,i.e. the desired set-point temperature at step n, but also to supply thecontrol circuit.

[0064] In FIG. 7 the scheme of block 510 that generates the desiredtemperature profiles is shown in more detail. In particular, block 510generates the correct sequence of set points that describe a desiredtemperature profile.

[0065] In practice, the temperature profile generator is an integrationalgorithm that can be described by the equation:

T _(set) ^((n)) =T _(set) ^((n−1)) +DT _(set) * t _(samp)  (5)

[0066] in which T_(set) ^((n)) is the desired temperature at step n,T_(set) ^((n−1)) is the temperature detected at the previous step n−1,DT_(set) is the rate of change of the temperature and t_(samp) is thesampling period.

[0067] Therefore, values DT_(set) and t_(samp), as well as initialtemperature value T_(init) that is only considered at the initial moment(step n=1) of the control, reach the integrator block 511 of FIG. 7.Logical operator 512 therefore represents a condition that occurs onlyat the initial moment, when it is necessary to know the startingtemperature.

[0068]FIG. 8 shows the predictive component 530 of the model or FFmodel. This model component is used to predict the power which needs tobe supplied to the system to obtain a given temperature T_(set) when thesystem is subject to a heating speed of DT_(set). In practice, the twocomponents—static power P_(S) (in constant temperature condition) anddynamic power P_(D) (in variable temperature condition whether linear ornon-linear)—to be supplied at step n are calculated taking account ofthe thermal resistance R_(th) and the thermal capacity C_(th) of thesystem, as well as the ambient temperature T_(amb) in which the systemoperates.

[0069] Static power P_(S) ^(FF) calculated according to the model FeedForward is given by the equation:

P _(S) ^(FF)=(T _(set) −T _(amb))*G _(th)  (6)

[0070] in which G_(th) is linked to the thermal resistance R_(th) by therelation:

G_(th)=(R _(th))⁻¹  (7)

[0071] In the model of FIG. 8, a subtraction operator 531 calculates thedifference between the set temperature T_(set) and the ambienttemperature T_(amb), while a multiplication operator 532 multiplies thedifference thus calculated by factor G_(th) to give static power P_(S)^(FF).

[0072] Dynamics power P_(D) ^(FF) calculated according to the FeedForward model instead is given by the equation:

P _(D) ^(FF) =DT _(set) *C _(th)  (8)

[0073] The values of C_(th) and R_(th) are recalculated at everyiteration of the model to follow the change of physical characteristicsof the system which vary with the varying temperature.

[0074] The model of FIG. 8 therefore provides for a multiplicationoperator 533 that multiplies factor DT_(set) and factor C_(th) to givedynamic power P_(D) ^(FF) calculated according to the Feed Forwardmodel.

[0075] The total power P^(FF) calculated according to the Feed Forwardmodel is given therefore by the sum of static power P_(S) ^(FF) and ofdynamic power P_(D) ^(FF), i.e.:

P ^(FF) =P _(S) ^(FF) +P _(D) ^(FF)  (9)

[0076] A sum operator 534 is therefore provided that calculates powerp^(FF) as output.

[0077]FIG. 9 shows the corrective component 550 of the model or FBmodel. In practice the Feed Back component of the model supplies acorrective effect on the power calculated in Feed Forward taking accountof the static temperature error Err_(T) and of its first derivativeDErr_(T) with respect to time.

[0078] In practice, factor Err_(T) is given by the difference betweenthe set-point temperature T_(set) ^((n−1)) set at the previous step andthe column temperature T_(c) ^((n−1)) effectively detected at the sameprevious step, i.e.:

Err_(T) =T _(set) ^((n−1)) −T _(c) ^((n−1))  (10)

[0079] The subtraction operator 551 shown in FIG. 9 calculates thisdifference.

[0080] In the correction of the power set at the step n, based ontemperature errors found at the previous step (n−1) account must howeverbe taken of the feedback system gain or, more properly, account must betaken separately of proportional gain GP^(FB) and derivative gainGD^(FB) of the Feed Back model.

[0081] The proportional contribution of the temperature error of ΔT_(P),calculated taking account of the proportional gain, is given by thefollowing relation:

ΔT _(P)=Err_(T) *GP ^(FB)  (11)

[0082] The two factors of the product, of which GP^(FB) represents adimensionless coefficient, are applied to the multiplication operator552 in FIG. 9.

[0083] The derivative contribution of the error of temperature ΔT_(D),calculated taking account of the derivative gain, is given by therelation:

ΔT _(D)=(dErr_(T) /dt)*GD ^(FB)  (12)

[0084] The two factors of the product (in this case GD^(FB) hasdimensions °C./sec), are applied to the multiplication operator 553.

[0085] The sum of contributions ΔT_(P) and ΔT_(D), obtained by means ofthe sum operator 554, is therefore multiplied by factor G_(th) throughthe multiplication operator 555, to give as output the corrective powerP^(FB) determined on the basis of the components of Feed Back model fromthe relation:

P ^(FB)=(ΔT _(P) +ΔT _(D))*G _(th)  (13)

[0086]FIG. 10 shows voltage actuator 570 of the supply voltage V_(sup)that allows to calculate the supply voltage to be applied to the entiresystem as a function of the power calculated on the basis of thepredictive model (p^(FF)) and the corrective model (P^(FB)), SO that thecolumn reaches the desired set-point temperature of T_(set) ^((n)) atstep n.

[0087] It should be emphasized that in the calculation of V_(sup) it isalso necessary to take account of the internal resistance R_(S) of thecontrol system. The value of R_(S) depends on the same control circuitand can also be affected for example by the construction of thepower/measurement terminals applied to the heating element of thecolumn.

[0088] The total power P_(set) to be applied to the system at step n isgiven by the sum of the power calculated on the basis of the predictiveand corrective models, i.e.:

P _(set)=(P ^(FF))+(P ^(FB))  (14)

[0089] Even if not expressly shown in FIG. 10, such powers can also be“weighted” before being added, in such a way as to privilege one or morecharacteristics with respect to others, for example the speed ofresponse with respect to the precision, or vice versa.

[0090] In the scheme of FIG. 10, a logical operator 572 could beprovided (even though it is not absolutely necessary) in series with thesum operator 571 predisposed to sum the factors (weighed or not) inrelation (14). This latter makes it possible (if necessary) to maintainnonetheless a minimal power P_(min) whenever the calculated powerP_(set) is less than the same minimal power.

[0091] The calculation of the voltage V_(set) to be applied to theheating element of the column at step n is preferably given by means ofthe relation:

V _(set)=(P _(set) *R _(c))^(½)  (15)

[0092] in which R_(c) is the resistance of the column, or rather of itsheating element, measured at the previous step (n−1). The multiplicationoperator 573 and the square root extraction operator 574 implement thisrelation.

[0093] The calculation according to relation (15) achieves betterprecision than other possible formulas because the resistance Rc variesvery little between successive sampling steps, even in case of suddenvariations of the desired heating speed. In fact, if for example,V_(set) were estimated as ratio between Pset (supply power at step n)and I_(c) (column current measured at step n−1) could give rise toproblems above all at the transient steps of P_(set) because of the highvariability of I_(c) between successive samplings.

[0094] As already mentioned previously, in order to obtain the totalsupply voltage V_(sup) at step n it is necessary to take account of theinternal resistance R_(s) of the system, i.e. the resistance measured atthe connection terminals of the heating element should ideally beremoved from the total circuit. The resistance R_(s) is generally muchsmaller than R_(c) and its variations therefore are still more limitedthan R_(c) between successive samplings

[0095] It is legitimate therefore to calculate the resistance R_(s) ofthe system at step n on the basis of the values V_(sup) ^((n−1)), V_(c)^((n−1)) and l_(c) ^((n−1)) measured at step (n−1) using the relation:

R _(s) ^((n))=(V _(sup) ^((n−1)) −V _(c) ^((n−1)))/l _(c) ^((n−1))  (16)

[0096] Consequently, the voltage V_(ps) ^((n)) of the system at step ncan therefore be calculated with limited error on the basis of therelation:

V _(s) ^((n)) =R _(s) ^((n)) *l _(c) ^((n−1))  (17)

[0097] The multiplication operator 575 supplies as output the valueV_(s) ^((n))—the product of the two factors indicated above—whichbecomes input for the sum operator 576 that finally supplies as outputthe value V_(sup) ^((n)) adding it to the value V_(set) ^((n))calculated for the column, i.e.:

V _(sup) ^((n)) =V _(set) ^((n)) +V _(s) ^((n))  (18)

[0098] The total voltage V_(sup) ^((n)) that the system must supply atstep n to give the necessary power to the same control circuit and thecolumn is thus calculated.

[0099] The cyclical updating of the values of thermal resistance R_(th)and thermal capacity C_(th) of the column can be accomplished at everystep in various ways.

[0100] For example, it has already been shown that the power P_(set)supplied to the column heating element in a certain step can beconsidered as the sum of the static power Ps and the dynamic powerP_(D). In practice, the power P_(set) ^((n−1)) that has been supplied atstep (n−1) will be given by the relation::

P _(set) ^((n−1)) =P _(S) ^((n−1)) +P _(D) ^((n−1))  (19)

[0101] Considering that the effects of the power supplied at step (n−1)are detected at the next step n, the relation that expresses the staticpower as a function of the new R_(th) ^((n)) parameter is the following:

P _(S) ^((n−1))=(T _(set) ^((n)) −T _(amb) ^((n)))/R _(th) ^((n))  (20)

[0102] in which T_(set) ^((n)) and T_(amb) ^((n)) represent respectivelythe desired column temperature at step n and the ambient temperature atstep n.

[0103] On the basis of the same consideration, the supplied dynamicpower at the step (n−1) is the following:

P _(D) ^((n−1))=(T _(set) ^((n)) −T _(set) ^((n−1)))/t _(samp) *C _(th)^((n))  (21)

[0104] in which T_(set) ^((n)) and T_(set) ^((n−1)) are the temperaturesdesired respectively at steps n and (n−1), and t_(samp) represents thesampling period.

[0105] Moreover, it is known that exists the following relation betweenR_(th) and C_(th):

τ=R _(th) *C _(th)  (22)

[0106] in which τ represents the mean delay within which the columnreaches a desired temperature T_(set), for example during a ramp. Inpractice, as it is also obvious from FIG. 11, the value τ can easily becalculated at any time taking account of the relation:

τ*(dT/dt)=Err_(T)  (23)

[0107] in which the factor dT/dt is the slope of the desired profile(the rate of change of temperature) and Err_(T) is the temperature errorat a certain step, i.e. the difference between the set temperatureT_(set) and the effective temperature T_(c) of the column.

[0108] Resolving equations (19)-(23) for R_(th) and C_(th), the newvalues of thermal resistance and thermal capacity are found that must beused in the model at step n, eventually providing also an opportuneweighted adaptation for these variable parameters. This represents,however, only one possibility of determination of the values of R_(th)and C_(th) and is supplied purely by way of example.

[0109]FIG. 12 shows a chromatogram of a test analysis carried out on amixture containing C₁₀-C₂₀ in C₆, employing H₂ as carrier.

[0110] The test was carried out using a capillary column 1.2 m inlength, with internal diameter of 0.25 μm and external diameter of 0.1mm. The gas chromatography apparatus was equipped with a split typeinjector with pressure of 114 kPa, flow of 1 cc/min at a temperature of250° C.; the output detector was of FID type maintained at a temperatureof 300° C.

[0111] The temperature profile was set up for 0.1 min to 80° C. and wasincreased until a temperature of 250° C. with a variation speed of 10°C./sec.

[0112] As can be seen in FIG. 12, in which the initial solvent part ofthe elution is not shown, the peaks of compounds C₁₀-C₂₀ are verynarrow, of the approximate order of {fraction (1/10)} second. Takingthis fact into consideration, and also the fact that the analysis onlylasts approximately 24 seconds, the peaks are very well defined, thusproving the validity of the temperature control system according to thepresent invention.

[0113] Furthermore, repeatability tests were done under the sameconditions reported above, for both the areas of the peaks and theretention times.

[0114] Table 1 shows the result of the tests done on 20 analyses ofsamples with the same C₁₀-C₂₀ composition to estimate the repeatabilityof the peak areas. TABLE 1 Mean Peak Area Relative Standard Compound(μVolt * sec) Deviation (%) C₁₀ 41840.5 1.44 C₁₂ 33701.8 1.71 C₁₄36509.6 1.53 C₁₆ 36838.4 1.59 C₁₈ 37024.6 1.99 C₂₀ 54709.7 2.1

[0115] Table 2 shows the result of the tests done on 20 analyses ofsamples with the same C₁₀-C₂₀ composition to estimate the repeatabilityof the retention times of the peaks. Retention times Relative StandardCompound (sec.) Deviation (%) C₁₀ 8.21 0.43 C₁₂ 12.31 0.32 C₁₄ 15.940.21 C₁₆ 18.88 0.17 C₁₈ 21.29 0.17 C₂₀ 23.34 0.13

[0116] As can be seen, results of both of the tests done show goodrepeatability of both parameters investigated.

[0117]FIG. 2 shows a circuit diagram of a temperature control systemaccording to the present invention. The system comprises in particular amain power section 21 that receives electrical power from a source, forexample the mains, and is able to distribute the voltage VSUp necessaryto the operation of the system, among which in particular the voltagenecessary to supply section 22 which supplies electrical power toheating element 100 of column 200.

[0118] The analogue value of voltage V_(C) applied to heating element100 is determined at the terminals of the same, while the analogue valueof current l_(c) that circulates in heating element 100 is determined bya measurement resistor 101 (or shunt) in the form of the voltage V_(l)at its terminals. The value of V_(C) measured at the terminals ofheating element 100 is preferably standardized with respect to thelength of the same element corresponding to section 102. Thisstandardized value is amplified in 103 before being converted to digitalform by an A/D converter 104 and being sent as input to amicro-controller or a DSP (Digital Signal Processor) indicated withreference 17. As already pointed out, the information on the length ofheating filament 100 can easily be calculated in the starting phase ofthe system and memorized in micro-controller or DSP 17, which then sendsit to block 102 through link 110.

[0119] The analogue value of I_(c), shown in the form of the voltageV_(l) across resistor 101, is amplified in 105 before being converted todigital form by an A/D converter 106 and being sent as input tomicro-controller or DSP 17.

[0120] Micro-controller or DSP 17 moreover also receives the value ofthe ambient temperature from sensor 15 under the form of a convertedanalogue signal that is first amplified in 107 and then converted intodigital form by an A/D converter 108.

[0121] Micro-controller or DSP 17 comprises two output lines 111 and 112that go respectively to control the main supply section 21, thatcommands the variation of the supply voltage V_(sup) to the system, andsupply section 22 which is designed to supply the correct voltage toheating element 100. Micro-controller or DSP 17 can moreover communicatethrough the bi-directional line 115 with an external unit 150 forprocessing or inputting data.

[0122] A possible embodiment of the present invention provides formicro-controller or DSP 17 moreover to control the electric motor of animpeller 130 through a suitable driver circuit 120. Alternatively, anelectro-valve can be set in action that controls the flow of a coolinggas. As shown in FIG. 5, the assembly constituted by filament 100,column 200 and the covering sheath 300 is preferably lodged in a slackway inside a tubular container 400 to allow the air moved by impeller130, or the cooling gas supplied through an appropriate electro-valve,to circulate in the space 403 comprised between the inner wall of thetubular covering 400 and the external wall of the covering sheath 300.Spacers 405 (shown by broken line in FIG. 5) can be associated tocontainer 400 with substantially radial alignment to avoid interruptionsof the airflow driven by impeller 130. According to this aspect of thepresent invention, it is possible to accelerate the cooling of column200.

1. A chromatography apparatus, of the type comprising at least onecapillary column and means for controlling the temperature of saidcolumn, characterized by comprising at least one element made ofelectrically conductive material to heat directly said at least onecapillary column and by said means for controlling the temperature ofsaid capillary column comprising a control device which operatesaccording to a mathematical model having one component of predictivetype, or Feed Forward type, which describes the thermodynamic behaviorof the assembly comprising said electrically conductive element and saidcolumn at least as a function of thermal resistance and thermal capacityof said assembly in order to regulate the supply of electrical powersupplied to said electrical conductor.
 2. An apparatus according toclaim 1, wherein said mathematical model further comprises a componentof corrective type, or Feed Back type.
 3. An apparatus according toclaim 1 or 2, wherein said device is apt to cyclically updates theparameters of said mathematical model.
 4. An apparatus according toclaim 1, wherein said means for controlling the temperature of saidcolumn comprise at least one device apt to cyclically determine thevoltage applied to the terminals of said conductive element and thecurrent that circulates in said conductive element.
 5. An apparatusaccording to claim 1, wherein said means for controlling the temperatureof said capillary column comprise at least one device apt to determinecyclically the electrical resistance of said electrically conductiveelement as a function of the voltage applied to the terminals of saidconductive element and the current that circulates in said conductiveelement.
 6. An apparatus according to claim 1, wherein said means forcontrolling the temperature of said capillary column comprise at leastone device apt to determine cyclically the temperature of said column asa function of the voltage applied to the terminals of said conductiveelement and the current that circulates in said conductive element. 7.An apparatus according to claim 1, characterized by further comprisingmeans for detecting the temperature of said column.
 8. An apparatusaccording to claim 7, wherein said means for detecting the temperatureof said column comprise said element in electrically conductive materialand wherein said at least one column and said at least one conductiveelement are disposed in a covering sheath in close mutual contact forall the length contained inside said sheath.
 9. An apparatus accordingto claim 1, wherein said element in electrically conductive material isproduced under the form of a filament.
 10. An apparatus according toclaim 8, wherein said covering sheath is made of an electricallyinsulating material.
 11. An apparatus according to claim 8, wherein saidcovering sheath is made of ceramic fibers.
 12. An apparatus according toclaim 8, wherein said covering sheath is made of a thermo-shrinking typematerial.
 13. An apparatus according to claim 8, characterized bycomprising a tubular container inside which the assembly constituted bysaid capillary column, said filament in conductive material and saidcovering sheath, is lodged in a slack way.
 14. An apparatus according toclaim 13, wherein means are provided for conveying and circulating athermal exchange fluid in the space comprised between the inner wall ofsaid tubular container and the external wall of said covering sheath.15. A method for controlling the temperature of a capillary column in achromatography apparatus, characterized by providing for the use atleast one element made of electrically conductive material for directlyheating said capillary column, and wherein the control of thetemperature is carried out according to a mathematical model having acomponent of predictive type, or Feed Forward, type, which describes thethermodynamic behavior of the assembly comprising said electricallyconductive element and said column at least as a function of thermalresistance and thermal capacity of said assembly in order to regulatethe supply of electrical power to said conductive element.
 16. A methodaccording to claim 15, wherein said mathematical model comprises afurther component of corrective type, or Feed Back type.
 17. A methodaccording to claim 15 or 16, wherein the parameters of said mathematicalmodel are cyclically updated.
 18. A method according to claim 15,wherein said capillary column and said conductive element are disposedinside a covering sheath in close mutual contact.
 19. A method accordingto claim 15, characterized by further providing for the measurement ofthe temperature of said column.
 20. A method according to claim 19,wherein the temperature of said column is detected by means of saidelement in electrically conductive material.
 21. A method according toclaim 15, wherein said element in electrically conductive material ismade in the form of a filament.
 22. A method according to claim 18,wherein said covering sheath is made of electrically insulatingmaterial.
 23. A method according to claim 22, wherein said coveringsheath is made of ceramic fibers.
 24. A method according to claim 22,wherein said covering sheath is made of a thermo-shrinking typematerial.
 25. A method according to claim 15, wherein the assemblyconstituted by said capillary column, said filament in conductivematerial and said covering sheath is lodged in a slack way inside atubular container.
 26. A method according to claim 25, wherein thecirculation of a thermal exchange fluid in the space comprised betweenthe inner wall of said tubular container and the external wall of saidcovering sheath is provided for.
 27. A method according to claim 17,wherein the parameters of said model are cyclically calculated andupdated on the basis of information relating to the temperature profilethat is desired to be obtained in the time, said information comprisingat least the instantaneous value of the temperature and at least theinstantaneous value of its derivative with respect to time.
 28. A methodaccording to claim 15, characterized by cyclically detecting the voltageapplied to the terminals of said conductive element and the current thatcirculates in said conductive element.
 29. A method according to claim15, characterized by cyclically determining the resistance of saidelectrical conductive element as a function of the voltage applied tothe terminals of said conductive element and of the current thatcirculates in said conductive element.
 30. A method according to claim15, characterized by cyclically determining the temperature inside saidcovering sheath as a function of the voltage applied to the terminals ofsaid conductive element and of the current that circulates in saidconductive element.